SPHERE PACKING NUMBERS FOR SUBSETS OF THE BOOLEAN n-CUBE WITH BOUNDED VAPNIK-CHERVONENKIS DIMENSION

  • Authors:

  • David Haussler

  • Affiliations:

  • -

  • Venue:
  • SPHERE PACKING NUMBERS FOR SUBSETS OF THE BOOLEAN n-CUBE WITH BOUNDED VAPNIK-CHERVONENKIS DIMENSION
  • Year:
  • 1991

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Abstract

Let V contained in {0,1}^n have Vapnk-Chervonenkis dimension d. Let M(k/n,V) denote the cardinality of the largest W contained in V such that any two distinct vectors in W differ on at least k indices. We show that M(k/n,V) = (cn/(k+d))^d for some constant c. This improves on the previous best result of ((cn/k)log(n/k))^d. This new result has applications in the theory of empirical processes.